On February 24, 2018, Davidson was traded by the Oilers to the New York Islanders in exchange for a 2019 third-round pick.[9] Davidson joined the Islanders for the final stretch of the season, appearing in 15 games and collecting a goal and assist as the club fell short of the post-season.

As an impending restricted free agent, Davidson was not tendered a qualifying offer by the Islanders resulting in his status as a free agent on June 25, 2018.[10] On August 28, 2018, it was announced that Davidson would attend the Chicago Blackhawks' training camp on a professional tryout.[11] On September 27, 2018, the Blackhawks signed Davidson to a one-year contract worth $650,000.[12]